Question

# Which of the following is the graph of the equation y = 3x - 2 in the *x y*-plane?

Hint:

**Hint:**

The graph of an equation is the representation of the equation on the xy -plane. We are given the equation of a line and we need to find its graphical representation. When a line cuts through x-axis, then the y -coordinate is 0 and when it cuts y -axis, the x -coordinate is 0 . We use this idea to check which of the graphs in the options satisfy the given equation.

## The correct answer is:

### We are given the equation

We find its x-intercept, that is, the point at which the line cuts x-axis.

To find x-intercept, we put y = 0 in the above equation.

So, we get

0 = 3x - 2

Simplifying, we get

Thus, the x-intercept is

Similarly, we find the y-intercept of the line, that is, the point at which the line cuts y-axis.

To find the y-intercept, we put x=0 in the above equation to get

Simplifying, we get

y = - 2

Thus, the y-intercept is .

In the graphs in the options above, we can see that graph B) has x-intercept less than 1 and y intercept -2.

The x-intercept that we found above is which is less than 1.

Thus, the correct option is B)

**Note:**

We can also solve this question by eliminating the options.

The first option A) is not correct because the line passes through the origin and so it must satisfy the equation, which is not true as 0- 2

Then C) is not correct as the line passes through (0, -3), but this point does not satisfy the equation. Similarly, for option D) the point (0, 2) lies on the graph, but does not satisfy the equation.

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### Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees' pollen grains per square centimeter that were deposited each year within layers of a lake's sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1% annual increase in the number of grains per square centimeter thereafter. Which of the following functions models p(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited?

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The system of equations above is graphed in the xy -plane. What is the x -coordinate of the intersection point ( x, y) of the system?

The system of equations above is graphed in the xy -plane. What is the x -coordinate of the intersection point ( x, y) of the system?

According to the system of equations above, what is the value of X ?

**Note:**

Here we find the value of *y* from equation (1) and use it in equation (2).

We could do it the other way and receive the same answer, that is, if we find the value of y from equation (2) and use it in equation (1) to find x, we get the same value of x as found in the solution above.

Students are encouraged to try this method too.

According to the system of equations above, what is the value of X ?

**Note:**

Here we find the value of *y* from equation (1) and use it in equation (2).

We could do it the other way and receive the same answer, that is, if we find the value of y from equation (2) and use it in equation (1) to find x, we get the same value of x as found in the solution above.

Students are encouraged to try this method too.